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D and E are points on the sides AB and AC respectively of a A

Question

$D$ and $E$ are points on the sides $A B$ and $A C$ respectively of a $Δ A BC$ such that $D E ∣∣ BC$ . If $\frac{A D}{D B} = \frac{4}{7}$ and $A C = 6.6 c m$ , find $A E$ .

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D

and

E

are points on the sides

A B

and

A C

respectively of a

Δ A BC

such that

D E ∣∣ BC

. If

\frac{A D}{D B} = \frac{4}{7}

and

A C = 6.6 c m

, find

A E

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Text solutionVerified

Given :

\frac{A D}{D B} = \frac{4}{7}

and

A C = 6.6 c m

Find :

A E

By BPT :

\frac{A D}{D B} = \frac{A E}{EC}

Add 1 on both sides

\frac{A D}{D B} + 1 = \frac{A E}{EC} + 1

\frac{( A D + D B )}{D B} = \frac{( A E + EC )}{EC}

\frac{( 4 + 7 )}{7} = \frac{A C}{EC} = \frac{6.6}{EC}

EC = \frac{( 6.6 \times 7 )}{11}

EC = 4.2 c m

And,

A E = A C - EC

A E = 6.6 - 4.2

AE = 2.4 \ cm

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Question Text	$D$ and $E$ are points on the sides $A B$ and $A C$ respectively of a $Δ A BC$ such that $D E ∣∣ BC$ . If $\frac{A D}{D B} = \frac{4}{7}$ and $A C = 6.6 c m$ , find $A E$ .
Answer Type	Text solution:1
Upvotes	150